Evolution of semilinear conormal waves
Existence of quasilinear relaxation shock profiles in systems with characteristic velocities
We revisit the existence problem for shock profiles in quasilinear relaxation systems in the case that the velocity is a characteristic mode, implying that the profile ODE is degenerate. Our result states existence, with sharp rates of decay and distance from the Chapman–Enskog approximation, of small-amplitude quasilinear relaxation shocks. Our method of analysis follows the general approach used by Métivier and Zumbrun in the semilinear case, based on Chapman–Enskog expansion and the macro–micro...
Formation and development of global shock for p-system
Formation of singularities for viscosity solutions of Hamilton-Jacobi equations
Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems
We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.
Formulation forte entropique de lois scalaires hyperboliques-paraboliques dégénérées
Front d'onde des fonctions non linéaires et polynômes
Fundamental solutions and singular shocks in scalar conservation laws.
We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0, related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks...
Generalized solutions to singular initial-boundary hyperbolic problems with non-lipshitz nonlinearities
Global in Time Stability of Steady Shocks in Nozzles
We prove global dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. One of the key improvements compared with previous results is that we assume neither the smallness of the slope of the nozzle nor the weakness of the shock strength. A key ingredient of the proof are the derivation a exponentially decaying energy estimates for a linearized problem.
Global solution to a Hopf equation and its application to non-strictly hyperbolic systems of conservation laws.
Global sound waves for quasilinear second order wave equations.
High resolution methods for the Buckley-Leverett equation.
Highfrequency asymptotics of the field scattered by an obstacle near tangential rays.
How parabolic free boundaries approximate hyperbolic fronts.
Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws.
Infinitely narrow soliton solutions to systems of conservation laws.
Interaction de chocs
Interaction d'ondes simples pour des équations complètement non-linéaires
Interaction d'ondes simples pour des équations complètement non-linéaires